Home
Class 12
MATHS
Prove that the value of each the followi...

Prove that the value of each the following determinants is zero:
`|sin^2(x+(3pi)/2)sin^2(x+(5pi)/2)sin^2(x+(7pi)/2)|`
`|sin^.(x+(3pi)/2)sin^.(x+(5pi)/2)sin^.(x+(7pi)/2) |`
`|sin^.(x-(3pi)/2)sin^.(x-(5pi)/2)sin^.(x-(7pi)/2)|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

sin^(3)x +sin^(3)(x-(2pi)/3) +sin^(3)(x+(2pi)/3)=0

Prove that: sin^2(pi/(18))+sin^2(pi/9)+sin^2((7pi)/(18))+sin^2((4pi)/9)=2

Find the critical points of each of the following functions : sin2x-x(-(pi)/(2)lexle(pi)/(2))

Find the value of sin^2(pi/16)+ sin^2 ((3pi)/16)+sin^2 ((5pi)/16)+sin^2((7pi)/16) .

sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

int_(0)^((pi)/(2))(sin^((3)/(2))x)/(sin^((3)/(2))x+cos^((3)/(2))x)dx

Prove that each of the following functions is strictly decreasing phi(x) = sin x(pi/2 le x le pi)

Prove that sin (pi/14)sin((3pi)/14)sin((5pi)/14)=1/8

Prove that, cos^(2) (pi/4) + sin^(2) (3pi/4) + sin^(2) (5pi/4) + sin^(2)(7pi/4) = 2 .

Show that : "sin" 2(pi)/(7)+ "sin"(4pi)/(7)-"sin" (6pi)/(7) =4 "sin" (pi)/(7) "sin" (2pi)/(7) "sin" (3pi)/(7)

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. The value of |y z z xx y p2p3r1 1 1|,w h e r ex ,y ,z are respectively...

    Text Solution

    |

  2. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

    Text Solution

    |

  3. Prove that the value of each the following determinants is zero: |s...

    Text Solution

    |

  4. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

  5. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

    Text Solution

    |

  6. " if " |{:(a^(2),,b^(2),,c^(2)),((a+1)^(2),,(b+1)^(2),,(c+1)^(2)),((a-...

    Text Solution

    |

  7. Statement 1: "Delta"= |[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m ...

    Text Solution

    |

  8. Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]|=2(a-b)(b...

    Text Solution

    |

  9. If =|sin theta cos var phi sin theta sin var phi cos theta cos theta c...

    Text Solution

    |

  10. The system of equations -2x+y+z=a, x-2y+z=b, x+y-2z=c, has: (a)no so...

    Text Solution

    |

  11. Show that if x1, x2, x3!=0 abs((x1+a1.b1,a1.b2,a1.b3),(a2.b1,x2+a2.b...

    Text Solution

    |

  12. If determinant |[cos(theta+phi),-sin(theta+phi),cos2phi],[sin theta,co...

    Text Solution

    |

  13. If Deltar =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1,...

    Text Solution

    |

  14. The values of k in R for which the system of equations x+k y+3z=0,k x...

    Text Solution

    |

  15. A determinant of second order is made with the elements 0 and 1. Fi...

    Text Solution

    |

  16. If a ,b , c are nonzero real numbers such that |[b c,c a, a b],[ c a, ...

    Text Solution

    |

  17. Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[...

    Text Solution

    |

  18. Consider the determinant f(x)=|[0,x^2-a, x^3-b], [x^2+a,0,x^2+c], [x^4...

    Text Solution

    |

  19. Find the value of |[1, 2, 4],[-1,3, 0],[4 ,1, 0]|

    Text Solution

    |

  20. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

    Text Solution

    |